Solve for $x$ and $y$ using elimination. ${4x-y = 24}$ ${-5x+y = -31}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {4x-y = 24}\thinspace$ to find $y$ ${4}{(7)}{ - y = 24}$ $28-y = 24$ $28{-28} - y = 24{-28}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 7}$ into $\thinspace {-5x+y = -31}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ + y = -31}$ ${y = 4}$